Model 3D SURFACE RECONSTRUCTION

2.2 Development of the underwater housing

The underwater housing was developed by the 4h Jena engineering GmbH 4h Jena 2015. It was conceived for both fresh and salt water use. In order to sustain the water pressure a maximal diving depth of 40 m was set. The housing material is the synthetic material PA 2200. The optical windows for the cameras, the projector, and the laser beams were produced from sapphire glass, and the window for the display from polycarbonate. The plane windows for the cameras and the projector were tilted according to the directions of the optical axis in order to simplify the calibration procedure see next section. For the realization of a sufficient heat removal from the housing appropriate heat sinks and a base plate with cooling ribs were constructed. Additionally, a separable under water plug-in connector cable was realized for the power supply and the signal lines. In order to provide a correct handling also with diver gloves, separable inductive switching boards including control keys and interfaces to the scanner were developed see Figure 3. Figure 4 shows a construction drawing and the scanner in the housing without back panel with the display. Figure 3. Housing views Figure 4. Housing views: construction draw, view from above left, sensor inside housing without back-panel right

3. 3D SURFACE RECONSTRUCTION

3.1 Model

The principle in order to obtain 3D measurement points is triangulation of corresponding points in the two cameras as well known in photogrammetry see e.g. Luhmann et al. 2006. However, because of the refraction of the rays at the interfaces between air, housing windows, and water, a simple transmission of the camera model would lead to considerable errors. Even if the parameters of the pinhole camera model are adapted to the underwater situation, the classical triangulation procedure would be erroneous without model extension. Hence, an extension of the typically used pinhole camera model is necessary. However, there is one case, where the pinhole model could be applied in the same manner. This could be achieved if we violate any refraction. This is obtained using spherical so called dome ports in the housing and placing the cameras exactly so, that the projection centre coincides with the centre point of the spheres fitted to the inner and outer dome port surface. Figure 5 illustrates this situation. In practical realizations of underwater cameras this principle has been applied, e.g. by Korduan Korduan et al. 2003. However as reported by Bruno Bruno et al. 2011, there occurred differences in the parameters of air and water calibration, probably due to deviations of the exact camera placement. Hence, additional correction parameters describing the distortion are necessary, probably depending on the object distance. Figure 5. Ray directions using spherical dome ports The second typical case of the housing interface is the use of plane glass see Figure 6. Here we can observe refraction according to Snell’s law which should be considered in the procedure of calculation of the 3D measurement points. Several authors have proposed appropriate extensions of the camera model in order to regard the refraction effects, e.g. Li Li et al. 1996, Kwon and Casebolt Kwon and Casebolt 2006, or Telem and Filin Telem and Filin 2011. Figure 6. Ray directions with refraction effects using planar glass interface An alternative is the initial usage of a different camera model, e.g. the ray-based model Wolf et al. 2007, Bothe et al. 2010 or the raxel camera model Grossberg and Nayar 2005. Some Authors suggest using the pinhole camera model with adapted parameters obtained by calibration using underwater images Fryer and Fraser 1986, Harvey and Shortis 1998, Costa et al. 2006. 3.2 Additional parameters In contrast to the direct linear ray propagation, the directions of the rays from the object points in the water change by refraction before they reach the image plane. The change of the direction depends on the glass thickness, the orientation of the cameras optical axis concerning the glass surface, and the distance of the cameras projection centre to the housing interface. This contribution has been peer-reviewed. doi:10.5194isprsarchives-XL-5-W5-33-2015 35 In our modelling we assume a perpendicular orientation of the camera concerning the glass surface see Figure 6. Hence, we have the additional parameters glass thickness th and interface distance d. These parameters have to be determined for both cameras. Additionally, the refraction indices of air n a , water n w , and the window glass n g must be known. In the following we assume to know the refraction indices n a =1.0, n w =1.334, n g =1.7 and the glass thickness th, which e.g. can be measured tactile using any precise measurement.

3.3 Corresponding point determination